Top scorer Scott Coupland got the only goal on Boxing Day as Deeping Rangers took their unbeaten run to 19 league games.
He was on target for the sixth successive game, taking the Clarets into the new year in third place thanks to five wins in a row in December.
Boss Michael Goode said: “It was a really hard-fought game in difficult conditions on a horrible pitch.
“We talked before kick-off about the importance of getting three points.
“After a slow start, we were looking pretty good and it was only a matter of time until we scored.
“Jason Kilbride put in a great ball and Coupland got a yard in front of a defender to turn in the header.
It was a professional performance where we had to dig in.Michael Goode
“Before the break we were fairly comfortable but in the second half Harrowby caused a few problems.
“Richard Stainsby made a great save from a free-kick then we upped the tempo and Will Bird hit the post.
“We need a clinical edge to kill off games but after that we managed the game well and kept the ball.
“It was a professional performance where we had to dig in.
“Last season we might have conceded a late goal or even lost that game. So that shows how far we’ve come now.”